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Popular >

derivative of 6e^{-x/2}

Solution

\frac{d}{d x} (6 e^{- \frac{x}{2}})

Solution

- 3 e^{- \frac{x}{2}}

Solution steps

\frac{d}{d x} (6 e^{- \frac{x}{2}})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 6 \frac{d}{d x} (e^{- \frac{x}{2}})

Apply the chain rule:

e^{- \frac{x}{2}} \frac{d}{d x} (- \frac{x}{2})

= e^{- \frac{x}{2}} \frac{d}{d x} (- \frac{x}{2})

\frac{d}{d x} (- \frac{x}{2}) = - \frac{1}{2}

= 6 e^{- \frac{x}{2}} (- \frac{1}{2})

Simplify

6 e^{- \frac{x}{2}} (- \frac{1}{2}) : - 3 e^{- \frac{x}{2}}

= - 3 e^{- \frac{x}{2}}

Popular Examples

integral of-3x^4-6x^2+8

\int - 3 x^{4} - 6 x^{2} + 8 d x

limit as x approaches 0 of xcsc(pix)

x \to 0 lim (x csc (π x))

limit as x approaches 1/3 of x^4

x \to \frac{1}{3} lim (x^{4})

limit as x approaches+0+of x^{sqrt(x)}

x \to + 0 + lim (x^{x})

limit as (x,y) approaches (0,0) of 1

(x, y) \to (0, 0) lim (1)

Frequently Asked Questions (FAQ)

What is the derivative of 6e^{-x/2} ?
The derivative of 6e^{-x/2} is -3e^{-x/2}
What is the first derivative of 6e^{-x/2} ?
The first derivative of 6e^{-x/2} is -3e^{-x/2}